1. Field of the Invention
This invention relates to a non-spectral filtering system and method for reducing random noise in signals.
2. Description of the Related Art
Noise plagues almost every modern digital and analog system in which some electrical signal must be transferred from one device to another. A car driver who tries to tune the radio to eliminate as much "static" as possible and the scientist who is attempting to build up a clear picture of a planet from the weak transmission of a distant satellite are both trying to increase the amount of the desired signal they get relative to the amount of undesired noise that accompanies the signal. Because of the great need to reduce the effect of noise, there are a very large number of noise-reduction techniques and systems.
The traditional approach to filtering out noise is spectral, that is, it is based on discovering which frequencies one expects the desired signal to have and then designing filters that remove all other frequencies. In a broad sense, a radio is a type of spectral filter--albeit a very sophisticated one--and is a common example of a device that lets through and amplifies signals within a certain narrow frequency band (corresponding to the selected radio station) and filters out other signals (corresponding to other radio stations or to noise) that aren't "close enough" to the selected frequency.
Spectral filters range from simple networks of common electrical components such as resistors, capacitors, and coils, to complicated digital systems, such as those used for high-speed conversion and transmission of long-distance telephone signals over fiber optic cables or via satellite. The book Digital Signal Processing, Oppenheim, A. V. and Schafer, R., Prentice Hall, Englewood Cliffs, N.J. (1974), is but one example of a well-known text that describes the techniques of modern digital signal processing.
Most signals that are processed in digital form start out as analog signals. For example, although there may be pauses in music played by an orchestra, most of the time there is some continuous sound being produced. In order to convert the continuous sound into a form suitable for manipulation by digital circuitry such as a CD player, known techniques are applied to "sample" the continuous sound signal into a series of numerical values. Then, numerical manipulations can be applied to the series to obtain results similar to or better than those one would get using physical analog devices such as capacitors and coils.
Conventional spectral approaches to digital filtering exploit the fact that random noise is distributed over an infinitely wide frequency range, while a noise-free signal is typically concentrated over a finite range of frequencies. Sampling the noisy signal at a high rate and filtering out all frequencies outside the range of frequencies of the noise-free signal thus filters out the noise strength that lies outside of that range. By increasing the sampling rate, increasingly large amounts of the noise can be suppressed.
When the noise-free signal is itself distributed over a large or infinite range of frequencies, very high sampling rates are required for the conventional filter to perform satisfactorily. Yet the noise-free signal may be compactly representable in some other, albeit non-spectral, form. If one could build a filter that worked in such a non-spectral form, a low sampling rate might suffice for satisfactory performance; however, little is known in the prior art about the design or analysis of such filters. In fact, much of the literature is limited to discussions of linear filters, that is, filters whose output bears a linear relation to their input so that scaling the input by a constant factor will cause the output to be scaled by the same factor. Spectral filters are linear filters, and it is widely understood that linear filters are a narrower and less powerful class of filters than non-linear filters.
One object of this invention is to provide a method for the design and realization of non-linear noise filtering systems. The method of the invention holds over a broad class of signals and includes choices that can be made by the user to enable simultaneous control over the sampling rate and the effectiveness of the filtering. Control over the sampling rate is made possible by the inventor's discovery of the link between data compression and noise filtering, used in conjunction with the well understood techniques for tailoring data compression systems to particular applications.